01234_01243_01324_01342_01423_01432_02134_02143_02314_02341_02413_02431_03124_03142_03214_03241_03412_03421_04123_04132_04213_04231_04312_04321_12034_12043_12340_12430_13024_13042_13240_13420_14023_14032_14230_14320_23041_23140_24031_24130

Counting sequence:
1, 1, 2, 6, 24, 80, 240, 700, 2016, 5724, 16040, 44484, 122352, 334204, 907480, 2451540, 6593344, 17663340, 47155752, 125502980, 333095440, 881853084, 2329366776, 6140182580, 16154850528, 42429700300, 111260640712, 291319949412, 761732957104, 1989211520764, 5188507821720, 13518271607956, 35184202016384, 91485005869356, 237658389920616, 616851366247620, 1599754131742032, 4145631703752540, 10735217369990200, 27779863414956276, 71839573202331680, 185663213068306828, 479545200602038536, 1237904002467160356, 3193812682671752944, 8235832996455968700, 21227121345582100952, 54685146755381574996, 140815679277598718400, 362446666883155333612, 932515990487900985000, 2398251432580693800324, 6165469209491080036496, 15844440658272654684188, 40703621917691420471160, 104529828635540778256820, 268351377562455344241504, 688698141209008065792588, 1766933894855935561514056, 4531923528957582314568164, 11620372900376735676713520, 29787695290120163543343228, 76337337800872008661024024, 195579856570387831925949972, 500958558899122641098951936, 1282842787238907109594690220, 3284295828776555861160473064, 8406425897059795104114716228, 21512146763059710546297463760, 55037941626094736750433812700, 140782730991638777600365451960, 360037674147856553372382130804, 920577483665767768083999329952, 2353363238437414572215855352588, 6015006179425509912373688334216, 15371062010581980744623073972900, 39273034276522901789567787093360, 100325155750115902431014554734908, 256242978177237470143087111915608, 654368997048627246984574955130580, 1670797680932118186617955396591680, 4265374308964355283639468878599020, 10887401412505667317557043896847656, 27786044603050676403583893699061508, 70903255367926244940910258440849168, 180902291483822105446557476201484700, 461489523916597963346585023755716088, 1177120440512097423277383263443983156, 3002082161185527526207492730014859744, 7655404823911519634952361208915626956, 19519060823984123191718352374161339080, 49761796789227360827797620279438699364, 126847158055616824747197762487476064432, 323306261602342745146623778722427634172, 823943200281479598318228965233080308632, 2099574448416880232707604317493148653460, 5349548874607543738354973169426937262976, 13628746514380034210343057492103187592236, 34717505147144821475857898566059551467624, 88429237570821566017004882236931419791300, 225215843534615687936073879904647222930000

Generating function in Maple syntax:
(4*x^6-10*x^5+14*x^4-9*x^3+9*x^2-5*x+1)/(2*x^3-2*x^2+3*x-1)^2

Generating function in latex syntax:
\frac{4 x^{6}-10 x^{5}+14 x^{4}-9 x^{3}+9 x^{2}-5 x +1}{\left(2 x^{3}-2 x^{2}+3 x -1\right)^{2}}

Generating function in sympy syntax:
(4*x**6 - 10*x**5 + 14*x**4 - 9*x**3 + 9*x**2 - 5*x + 1)/(2*x**3 - 2*x**2 + 3*x - 1)**2

Implicit equation for the generating function in Maple syntax:
(2*x^3-2*x^2+3*x-1)^2*F(x)-4*x^6+10*x^5-14*x^4+9*x^3-9*x^2+5*x-1 = 0

Implicit equation for the generating function in latex syntax:
\left(2 x^{3}-2 x^{2}+3 x -1\right)^{2} F \! \left(x \right)-4 x^{6}+10 x^{5}-14 x^{4}+9 x^{3}-9 x^{2}+5 x -1 = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,1,-11/2548*n*((((182/33*I*2^(1/3)-7/132*2^(5/6)*13^(1/2))*3^(1/2)-7/44*I*2^(5/6)*13^(1/2)+182/33*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-1274/33+((-13/132*I*2^(2/3)-1/3*13^(1/2)*2^(1/6))*3^(1/2)+I*13^(1/2)*2^(1/6)+13/132*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/588*(-49*I*3^(1/2)-49)*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3+1/588*(-9*2^(1/6)*(I-1/3*3^(1/2))*13^(1/2)+(2*I*3^(1/2)-2)*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))^(-n)+(((-182/33*I*2^(1/3)-7/132*2^(5/6)*13^(1/2))*3^(1/2)+7/44*I*2^(5/6)*13^(1/2)+182/33*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-1274/33+((-1/3*13^(1/2)*2^(1/6)+13/132*I*2^(2/3))*3^(1/2)-I*13^(1/2)*2^(1/6)+13/132*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/588*(49*I*3^(1/2)-49)*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3+1/588*(9*2^(1/6)*(I+1/3*3^(1/2))*13^(1/2)+(-2*I*3^(1/2)-2)*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))^(-n)+2/3*((7/44*2^(5/6)*13^(1/2)*3^(1/2)-182/11*2^(1/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)-637/11+(13^(1/2)*3^(1/2)*2^(1/6)-13/44*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3))*(1/294*(-3*13^(1/2)*3^(1/2)*2^(1/6)+2*2^(2/3))*(4+3*13^(1/2)*2^(1/2)*3^(1/2))^(2/3)+1/6*(8+6*13^(1/2)*2^(1/2)*3^(1/2))^(1/3)+1/3)^(-n)))

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ -\frac{11 n \left(\left(\left(\left(\frac{182 i 2^{\frac{1}{3}}}{33}-\frac{7 \,2^{\frac{5}{6}} \sqrt{13}}{132}\right) \sqrt{3}-\frac{7 i 2^{\frac{5}{6}} \sqrt{13}}{44}+\frac{182 \,2^{\frac{1}{3}}}{33}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{1274}{33}+\left(\left(-\frac{13 i 2^{\frac{2}{3}}}{132}-\frac{\sqrt{13}\, 2^{\frac{1}{6}}}{3}\right) \sqrt{3}+i \sqrt{13}\, 2^{\frac{1}{6}}+\frac{13 \,2^{\frac{2}{3}}}{132}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(-49 i \sqrt{3}-49\right) \left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{588}+\frac{1}{3}+\frac{\left(-9 \,2^{\frac{1}{6}} \left(i-\frac{\sqrt{3}}{3}\right) \sqrt{13}+\left(2 i \sqrt{3}-2\right) 2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{588}\right)^{-n}+\left(\left(\left(-\frac{182 i 2^{\frac{1}{3}}}{33}-\frac{7 \,2^{\frac{5}{6}} \sqrt{13}}{132}\right) \sqrt{3}+\frac{7 i 2^{\frac{5}{6}} \sqrt{13}}{44}+\frac{182 \,2^{\frac{1}{3}}}{33}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{1274}{33}+\left(\left(-\frac{\sqrt{13}\, 2^{\frac{1}{6}}}{3}+\frac{13 i 2^{\frac{2}{3}}}{132}\right) \sqrt{3}-i \sqrt{13}\, 2^{\frac{1}{6}}+\frac{13 \,2^{\frac{2}{3}}}{132}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(49 i \sqrt{3}-49\right) \left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{588}+\frac{1}{3}+\frac{\left(9 \,2^{\frac{1}{6}} \left(i+\frac{\sqrt{3}}{3}\right) \sqrt{13}+\left(-2 i \sqrt{3}-2\right) 2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{588}\right)^{-n}+\frac{2 \left(\left(\frac{7 \,2^{\frac{5}{6}} \sqrt{13}\, \sqrt{3}}{44}-\frac{182 \,2^{\frac{1}{3}}}{11}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}-\frac{637}{11}+\left(\sqrt{13}\, \sqrt{3}\, 2^{\frac{1}{6}}-\frac{13 \,2^{\frac{2}{3}}}{44}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(-3 \sqrt{13}\, \sqrt{3}\, 2^{\frac{1}{6}}+2 \,2^{\frac{2}{3}}\right) \left(4+3 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{2}{3}}}{294}+\frac{\left(8+6 \sqrt{13}\, \sqrt{2}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}\right)^{-n}}{3}\right)}{2548} & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 240
a(n+6) = -4*a(n)+8*a(n+1)-16*a(n+2)+16*a(n+3)-13*a(n+4)+6*a(n+5), n >= 7

Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 80
a(6) = 240
a{\left(n + 6 \right)} = - 4 a{\left(n \right)} + 8 a{\left(n + 1 \right)} - 16 a{\left(n + 2 \right)} + 16 a{\left(n + 3 \right)} - 13 a{\left(n + 4 \right)} + 6 a{\left(n + 5 \right)}, \quad n \geq 7

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/24574/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[23,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[16,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[4,x]
F[15,x] = F[4,x]
F[16,x] = F[11,x]+F[17,x]
F[17,x] = F[18,x]+F[19,x]+F[21,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[4,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[15,x]
F[23,x] = F[2,x]+F[24,x]
F[24,x] = F[114,x]+F[18,x]+F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[27,x]+F[36,x]
F[27,x] = F[28,x]+F[7,x]
F[28,x] = F[18,x]+F[29,x]+F[33,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[11,x]+F[17,x]
F[32,x] = F[17,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[16,x]+F[35,x]
F[35,x] = F[17,x]
F[36,x] = F[24,x]+F[37,x]
F[37,x] = F[104,x]+F[111,x]+F[18,x]+F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[48,x]
F[40,x] = F[28,x]+F[41,x]
F[41,x] = F[18,x]+F[42,x]+F[44,x]+F[46,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[17,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[32,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[35,x]
F[48,x] = F[37,x]+F[49,x]
F[49,x] = F[101,x]+F[18,x]+F[50,x]+F[54,x]+F[98,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[41,x]
F[53,x] = F[49,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[18,x]+F[57,x]+F[58,x]+F[95,x]
F[57,x] = 0
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[70,x]
F[63,x] = F[4,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[4,x]+F[68,x]
F[68,x] = F[19,x]
F[69,x] = F[68,x]
F[70,x] = F[60,x]+F[71,x]
F[71,x] = 2*F[18,x]+F[72,x]+F[92,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[80,x]
F[74,x] = F[64,x]+F[75,x]
F[75,x] = 2*F[18,x]+F[76,x]+F[78,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[68,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[69,x]
F[80,x] = F[71,x]+F[81,x]
F[81,x] = 2*F[18,x]+F[82,x]+F[86,x]+F[89,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[75,x]
F[85,x] = F[81,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[58,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[88,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[91,x]+F[94,x]
F[94,x] = F[60,x]+F[88,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[60,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]
F[100,x] = F[56,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]
F[103,x] = F[56,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[100,x]+F[106,x]
F[106,x] = F[107,x]+F[56,x]
F[107,x] = F[108,x]+F[18,x]+F[61,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[97,x]
F[110,x] = F[2,x]+F[60,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[103,x]+F[113,x]
F[113,x] = F[107,x]+F[56,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[113,x]+F[116,x]
F[116,x] = F[107,x]+F[2,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{23}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{16}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{114}\! \left(x \right)+F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{36}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{11}\! \left(x \right)+F_{17}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{104}\! \left(x \right)+F_{111}\! \left(x \right)+F_{18}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{48}\! \left(x \right)
F_{40}\! \left(x \right) = F_{28}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{18}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{32}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{35}\! \left(x \right)
F_{48}\! \left(x \right) = F_{37}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{101}\! \left(x \right)+F_{18}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)+F_{98}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{41}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{57}\! \left(x \right)+F_{58}\! \left(x \right)+F_{95}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{70}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right)
F_{69}\! \left(x \right) = F_{68}\! \left(x \right)
F_{70}\! \left(x \right) = F_{60}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{72}\! \left(x \right)+F_{92}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{74}\! \left(x \right) = F_{64}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{68}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{69}\! \left(x \right)
F_{80}\! \left(x \right) = F_{71}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{75}\! \left(x \right)
F_{85}\! \left(x \right) = F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{58}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{91}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{60}\! \left(x \right)+F_{88}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{60}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{56}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{56}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{100}\! \left(x \right)+F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{56}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{18}\! \left(x \right)+F_{61}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{97}\! \left(x \right)
F_{110}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{103}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{107}\! \left(x \right)+F_{56}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{107}\! \left(x \right)+F_{2}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_23(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_16(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_4(x))
Eq(F_15(x), F_4(x))
Eq(F_16(x), F_11(x) + F_17(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_21(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_4(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_15(x))
Eq(F_23(x), F_2(x) + F_24(x))
Eq(F_24(x), F_114(x) + F_18(x) + F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_27(x) + F_36(x))
Eq(F_27(x), F_28(x) + F_7(x))
Eq(F_28(x), F_18(x) + F_29(x) + F_33(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_11(x) + F_17(x))
Eq(F_32(x), F_17(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_16(x) + F_35(x))
Eq(F_35(x), F_17(x))
Eq(F_36(x), F_24(x) + F_37(x))
Eq(F_37(x), F_104(x) + F_111(x) + F_18(x) + F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_48(x))
Eq(F_40(x), F_28(x) + F_41(x))
Eq(F_41(x), F_18(x) + F_42(x) + F_44(x) + F_46(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_17(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_32(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_35(x))
Eq(F_48(x), F_37(x) + F_49(x))
Eq(F_49(x), F_101(x) + F_18(x) + F_50(x) + F_54(x) + F_98(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_41(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_18(x) + F_57(x) + F_58(x) + F_95(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_70(x))
Eq(F_63(x), F_4(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_4(x) + F_68(x))
Eq(F_68(x), F_19(x))
Eq(F_69(x), F_68(x))
Eq(F_70(x), F_60(x) + F_71(x))
Eq(F_71(x), 2*F_18(x) + F_72(x) + F_92(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_80(x))
Eq(F_74(x), F_64(x) + F_75(x))
Eq(F_75(x), 2*F_18(x) + F_76(x) + F_78(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_68(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_69(x))
Eq(F_80(x), F_71(x) + F_81(x))
Eq(F_81(x), 2*F_18(x) + F_82(x) + F_86(x) + F_89(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_75(x))
Eq(F_85(x), F_81(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_58(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_88(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_91(x) + F_94(x))
Eq(F_94(x), F_60(x) + F_88(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_60(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_56(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_56(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_100(x) + F_106(x))
Eq(F_106(x), F_107(x) + F_56(x))
Eq(F_107(x), F_108(x) + F_18(x) + F_61(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_97(x))
Eq(F_110(x), F_2(x) + F_60(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_103(x) + F_113(x))
Eq(F_113(x), F_107(x) + F_56(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_113(x) + F_116(x))
Eq(F_116(x), F_107(x) + F_2(x))
Pack JSON:
{"name": "point_placements", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "PointCorroborationFactory", "ignore_parent": true}], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "strategy_class": "RowColumnSeparationStrategy", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "strategy_class": "InsertionEncodingVerificationStrategy", "ignore_parent": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "OneByOneVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}, {"class_module": "tilings.strategies.verification", "strategy_class": "LocallyFactorableVerificationStrategy", "ignore_parent": false, "basis": [], "symmetry": false}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": false, "maxreqlen": 1, "extra_basis": [], "one_cell_only": false}, {"class_module": "tilings.strategies.requirement_placement", "strategy_class": "PatternPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0, 1, 2, 3], "point_only": false}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 4, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 4, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 4, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 4, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], 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